In a large skillet, heat the oil over medium-high heat. Add the chicken and cook, turning occasionally, until no longer pink in the center and juices run clear, 8 to 10 minutes. Remove from the heat and set aside to cool. In the bowl of an electric mixer, beat the egg whites on medium speed until stiff peaks form. Gradually add the sugar, beating after each addition until the mixture is light and fluffy, about 1 minute. Pour the cooled mixture into the skillet and stir to combine. Serve the sticky orange chicken with the nectarines.